Stochastic Models for Time Series. 1st ed. 2018

種類:

電子ブック

責任表示:

by Paul Doukhan

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Doukhan, Paul.
• SpringerLink (Online service)

シリーズ名:

Mathématiques et Applications ; 80

ISBN:

9783319769387 [3319769383]    

注記:

Part I Independence and Stationarity -- 1 Probability and Independence -- 2 Gaussian convergence and inequalities -- 3 Estimation concepts -- 4 Stationarity -- Part II Models of time series -- 5 Gaussian chaos -- 6 Linear processes -- 7 Non-linear processes -- 8 Associated processes -- Part III Dependence -- 9 Dependence -- 10 Long-range dependence -- 11 Short-range dependence -- 12 Moments and cumulants -- Appendices -- A Probability and distributions -- B Convergence and processes -- C R scripts used for the gures -- Index- List of figures.
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit

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